Sets of connecting units that may be joined to form structures are known and are often (but not always) sold as toys. The pieces in these sets typically favor one direction when adding pieces to a structure. For example, most common LEGO® bricks are joined by stacking one brick atop one or more others. Such sets may also require many different shapes of pieces to provide more flexibility in building. A set of connection units that supported building in multiple styles and directions using only a minimal number of different shapes would facilitate creating new kinds of structures and, as toys, would provide new opportunities for learning and creative expression.